If you take an example of tabstops being set at n=8, for example, the if the input has 1 character, the tab will add 7 spaces (to bring you to column 9). Basically, don't always add n spaces, add the number of spaces that brings you to the appropriate column for your particular value of n.
For example:
1
1234567890123456789
1------>
123---->
More words----->
"Assume a fixed set of tab stops" is for non-programmers, basically. We're used to a tab always aligning on a multiple of 4,8,etc. But in word processors, the tab stops are configurable... so the first tab would align you on column 6, the second would go to 30 (for example to sloppily center text) and the third would give you column 70 (for page numbers or something). He's just specifying here that we're talking about "programmer" tabstops, not a word processor's tabstops.